Analyzing three-dimensional transient heat conduction problems with the dimension splitting reproducing kernel particle method

Peng, Piaopiao; Cheng, Yumin

doi:10.1016/j.enganabound.2020.09.011

Cited by 21 publications

(4 citation statements)

References 45 publications

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“…Researchers have been studying the improved algorithms based on the RKPM and MLS frameworks. It is the final objective to retain high accuracy and decrease the computational disadvantages of these improved algorithms [32][33][34].…”

Section: High-accuracy Sph Algorithmsmentioning

confidence: 99%

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Wang

Yang

et al. 2023

Acta Mech. Sin.

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Smoothed particle hydrodynamics (SPH), as one of the earliest meshfree methods, has broad prospects in modeling a wide range of problems in engineering and science, including extremely large deformation problems such as explosion and high velocity impact. This paper aims to provide a comprehensive overview on the recent advances of SPH method in the fields of fluid, solid, and biomechanics. First, the theory of SPH is described, and improved algorithms of SPH with high accuracy are summarized, such as the finite particle method (FPM). Techniques used in SPH method for simulating fluid, solid and biomechanics problems are discussed. The δ -SPH method and Godunov SPH (GSPH) based on the Riemann model are described for handling instability issues in fluid dynamics. Next, the interface contact algorithm for fluid-structure interaction is also discussed. The common algorithms for improving the tensile instability and the framework of total Lagrangian SPH are examined for challenging tasks in solid mechanics. In terms of biomechanics, the governing equations and the coupling forces based on SPH method are exemplified. Then, various typical engineering applications and recent advances are elaborated. The application of fluid mainly depicts the interaction between fluid and rigid body as well as elastomer, while some complicated fluid-structure interaction ocean engineering problems are also presented. In the aspect of solid dynamics, galaxy, geotechnical mechanics, explosion and impact, and additive manufacturing are summarized. Furthermore, the recent advancements of SPH method in biomechanics, such as hemodynamically and gut health, are discussed in general. In addition, to overcome the limitations of computational efficiency and computational scale, the multiscale adaptive resolution, the parallel algorithm and the automated mesh generation are addressed. The development of SPH software in China and abroad is also summarized. Finally, the challenging task of SPH method in the future is summarized. In future research work, the establishment of multi-scale coupled SPH model and deep learning technology in solid and biodynamics will be the focus of expanding the engineering applications of SPH methods.

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Section: High-accuracy Sph Algorithmsmentioning

confidence: 99%

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

Wang

Yang

et al. 2023

Acta Mech. Sin.

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“…To improve the computational efficiency of the EFG method, by introducing the dimension splitting method [43], Cheng et al proposed the dimension splitting element-free Galerkin (DS-EFG) method [44] and dimension splitting interpolating element-free Galerkin (DS-IEFG) method [45]. The dimension splitting meshless method greatly improves the computational efficiency of the EFG method, and shows high computational efficiency and accuracy for 3D advection-diffusion problems [46], 3D transient heat conduction problems [47][48][49], 3D elasticity problems [50], 3D wave equations [51,52], etc.…”

Section: Introductionmentioning

confidence: 99%

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

Wang¹,

Wu²,

Xu³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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By introducing the dimensional splitting (DS) method into the multiscale interpolating element-free Galerkin (VMIEFG) method, a dimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method is proposed for three-dimensional (3D) singular perturbed convection-diffusion (SPCD) problems. In the DS-VMIEFG method, the 3D problem is decomposed into a series of 2D problems by the DS method, and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method. The improved interpolation-type moving least squares (IIMLS) method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems. The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems. The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes. For extremely small singular diffusion coefficients, the numerical solution will avoid numerical oscillation and has high computational stability. KEYWORDSDimension-splitting multiscale interpolating element-free Galerkin (DS-VMIEFG) method; interpolating variational multiscale element-free Galerkin (VMIEFG) method; dimension splitting method; singularly perturbed convection-diffusion problems

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“…By combining the traditional finite difference method with various kinds of meshless methods, thus the hybrid EFG method [26][27][28][29], the dimensional splitting complex variable EFG method [30][31][32][33][34], the dimension split reproducing kernel particle method [35][36][37][38] and the hybrid generalized interpolated EFG method [39] are proposed respectively, these methods can solve the multi-dimensional problems efficiently.…”

Section: Introductionmentioning

confidence: 99%

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

Cheng¹,

Xing²,

Peng³

2022

Computer Modeling in Engineering &Amp; Sciences

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In this paper, we considered the improved element-free Galerkin (IEFG) method for solving 2D anisotropic steadystate heat conduction problems. The improved moving least-squares (IMLS) approximation is used to establish the trial function, and the penalty method is applied to enforce the boundary conditions, thus the final discretized equations of the IEFG method for anisotropic steady-state heat conduction problems can be obtained by combining with the corresponding Galerkin weak form. The influences of node distribution, weight functions, scale parameters and penalty factors on the computational accuracy of the IEFG method are analyzed respectively, and these numerical solutions show that less computational resources are spent when using the IEFG method.

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Analyzing three-dimensional transient heat conduction problems with the dimension splitting reproducing kernel particle method

Cited by 21 publications

References 45 publications

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

On methodology and application of smoothed particle hydrodynamics in fluid, solid and biomechanics

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

The Improved Element-Free Galerkin Method for Anisotropic Steady-State Heat Conduction Problems

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